class: center, middle, inverse, title-slide .title[ # Lecture 24 ] .subtitle[ ## MLR with Categorical Variables: Interactions ] .author[ ### Psych 10 C ] .institute[ ### University of California, Irvine ] .date[ ### 05/25/2022 ] --- ## Model comparison: Simple linear regression models - Last class we looked at the predictions of each of the following models: -- - Null: `$$\text{Correct}_i \sim \text{Normal}(\beta_0, \sigma_1^2)$$` -- - Age: `$$\text{Correct}_i \sim \text{Normal}(\beta_0+\beta_1\text{age-group}_i, \sigma_2^2)$$` -- - Time: `$$\text{Correct}_i \sim \text{Normal}(\beta_0+\beta_2\text{time}_i, \sigma_3^2)$$` --- ## Model Comparison: Multiple linear regression models - Age and Time additive: `$$\text{Correct}_i \sim \text{Normal}(\beta_0+\beta_1\text{age-group}_i+\beta_2\text{time}_i, \sigma_4^2)$$` - Age and Time interaction: `$$\text{Correct}_i \sim \text{Normal}(\beta_0+\beta_1\text{age-group}_i+\beta_2\text{time}_i+\beta_3\text{age-group}_i\text{time}_i, \sigma_5^2)$$`